Permeability tensor for discontinuous rock masses

Abstract

Rock masses, which commonly contain a large number of discontinuities, are treated as homogeneous, anisotropic porous media to formulate the corresponding permeability tensor. This has been successfully achieved by introducing a symmetric tensor (crack tensor) which depends only on the geometry of the related cracks (aperture, size and orientation). The principal directions associated with the symmetric crack tensor are coaxial with those of the permeability tensor. The first invariant of the crack tensor is proportional to the mean permeability, while the deviatoric part is related to the anisotropic permeability. These results are well supported by numerical experiments on the permeability of cracked media by Long, Remer, Wilson and Witherspoon. An actual rock mass (moderately jointed granite) was studied to see whether the crack tensor can be determined in situ. Stereology, based on geometrical statistics, provides a sound basis for determining the crack tensor in situ. The crack tensor is obtained by treating statistically the crack orientation data presented via a stereographic projection together with the detailed mapping of crack traces visible on rock exposures. Des masses rocheuses, qui contiennent généalement un grand nombre de discontinuités, sont traitées comme des matiéres poreuses anisotropes homogénes pour formuler le tenseur de perméabilité correspondante. Ceci a été obtenu en introduisant un tenseur symétrique (tenseur de fissure) qui ne dépend que de la géometrie des fissures associées (ouverture, grandeur et orientation). Les directions principales associées avec le tenseur symétrique des fissures sont coaxiales avec celles du tenseur de perméabilité. Le premier invariant du tenseur des fissures est proportionnel à la perméabilité moyenne, tandis que la partie déviatorique est reliée à la perméabilité anisotrope. Ces résultats sont clairement confirmés par de nombreuses expériences sur la perméabilité des matiéres fissurées effectuées par Long, Remer, Wilson et Witherspoon. Une masse rocheuse (granit modérement fracturé) a été étudiée pour découvrir si on pouvait déterminer le tenseur des fissures en place. La stérologie, basée sur la statistique géometrique, fournit une base valable pour determiner le tenseur des fissures en place. Le tenseur des fissures est obtenu par le traitement statistique des données de l'orientation des fissures présentées par projection stéréographique, accompagné du relevé detail1é des traces de fissures visibles sur les roches exposées.

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

“…They applied the similar concept of wellbore productivity index introduced by Peaceman (1978Peaceman ( , 1983 and Lee and Milliken (1993) In the studies conducted by Lee et al (2001) and Li and Lee (2008) by a discrete fracture model (Clemo and Smith, 1997;Lee et al, 2001). In order to homogenize small-scale fractures, Oda (1985) derived a simple analytical expression for enhanced matrix permeability for gridblocks that contain very short fractures. Likewise, Lough et al (1997Lough et al ( , 1998 developed a boundary element method (with uniform pressure and periodic boundary conditions) to calculate effective conductivity for gridblocks containing multiple fractures.…”

Characteristics of Block Hydraulic Conductivity of 2-D DFN System According to Block Size and Fracture Geometry

“…해석영역은 블록의 크기가 DFN의 수리적 특성에 미 치는 영향을 파악하기 위하여 Table 1의 18개 (Kantani, 1984, Oda, 1985. (Kantani, 1984).…”

Joint Inversion of Fracture Model Properties for CO2Storage Monitoring or Oil Recovery History Matching

“…Equivalent permeability tensors are computed using analytical expressions based on the Oda's method [26]. If the statistical properties of the DFN are known, these properties can be directly integrated to obtain the equivalent permeability tensor [27].…”

“…In the contrary case, each fracture is studied separately. The equivalent permeability tensor is derived from the dips, strikes and volumes of the fractures [26]. Basic assumptions for this model are:…”